writing correction

docs/report/999.ipynb

@@ -25,13 +25,9 @@
     ":::{card} PWA101: Amplitude Analysis with Python basics\n",
     "TR-999\n",
     "^^^\n",
-    "This document serves as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.\n",
-    "Basic Python programming and libraries (e.g. `numpy`, `scipy`, etc.) are used to illustrate the general process in PWA.\n",
-    "Before advancing to the complexities of symbolic expressions (computations) with `sympy`, this tutorial aims to equip readers with a basic understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example.\n",
+    "This document serves as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model. Basic Python programming and libraries (e.g. `numpy`, `scipy`, etc.) are used to illustrate the general process and full workflow of PWA  in the context of hadron physics.\n",
     "+++\n",
-    "✅ [ComPWA/RUB-EP1-AG#93](https://github.com/ComPWA/RUB-EP1-AG/issues/93), [com\n",
-    "I\n",
-    "pwa.github.io#217](https://github.com/ComPWA/compwa.github.io/pull/217)\n",
+    "✅ [ComPWA/RUB-EP1-AG#93](https://github.com/ComPWA/RUB-EP1-AG/issues/93), [compwa.github.io#217](https://github.com/ComPWA/compwa.github.io/pull/217)\n",
     ":::\n",
     "::::"
    ]
@@ -66,7 +62,7 @@
    "source": [
     "- This document serves as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.\n",
     "- Basic Python programming and libraries (e.g. `numpy`, `scipy`, etc.) are used to illustrate the general process in PWA.\n",
-    "- Before advancing to the complexities of symbolic expressions (computations) with `sympy`.\n",
+    "- Before advancing to the complexities of symbolic expressions (computations) with e.g. `sympy` later, and as a comparison .\n",
     "- This tutorial aims to equip readers with a basic understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example."
    ]
   },
@@ -127,7 +123,7 @@
     "<!-- cspell:ignore Mathieu -->\n",
     "This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu.\n",
     "\n",
-    "The (photo-production) reaction is $ \\gamma p \\to \\eta \\pi^0 p$, it is described by an amplitude model with three possible resonances: $a_2$, $\\Delta^+$, and $N^*$. "
+    "The photo-production reaction is $ \\gamma p \\to \\eta \\pi^0 p$, which is one of the reaction channels in experiment such as [the GlueX experiment](http://www.gluex.org/). The decays are described by an amplitude model with three possible resonances: $a_2$, $\\Delta^+$, and $N^*$. "
    ]
   },
   {
@@ -384,7 +380,7 @@
     "tags": []
    },
    "source": [
-    "The [GlueX](http://www.gluex.org/) experiment at Jefferson Lab uses a fixed target with a linearly polarized photon beam, and the beam energy range in lab frame is typically from [**8 to 9 GeV**](https://doi.org/10.7566/JPSCP.26.022002).\n",
+    "The [GlueX](http://www.gluex.org/) experiment at Jefferson Lab uses a fixed proton target with a linearly polarized photon beam, and the beam energy range in the lab frame is typically from [**8 to 9 GeV**](https://doi.org/10.7566/JPSCP.26.022002).\n",
     "\n",
     "In the following, the variables without labelling of 'lab' is in the CM frame, those with labels of 'lab' is in the lab frame."
    ]
@@ -396,6 +392,7 @@
    },
    "source": [
     "We use the $\\gamma$ beam energy in the lab frame as the input:\n",
+    "\n",
     "$$\n",
     "E_{\\gamma, lab} = 8.5 \\; GeV\n",
     "$$  \n",
@@ -411,13 +408,16 @@
     "with $m_p$ is the proton mass\n",
     "\n",
     "We have the total four-momentum in lab frame:\n",
+    "\n",
     "$p_{tot,lab} = p_{\\gamma,lab} + p_{p,lab}$\n",
     "\n",
     "$E_{p} = \\sqrt { p_{p}^2+ m_{p}^2}$\n",
     "\n",
     "From the **lab frame** perspective, the CM total energy with expression in quantities from the **lab frame** is thus:\n",
     "\n",
-    "$\\sqrt{s} = E_0 = m_0 = \\sqrt{2 E_{\\gamma,lab}m_p+m_p^2}$"
+    "$$\n",
+    "\\sqrt{s} = E_0 = m_0 = \\sqrt{2 E_{\\gamma,lab} m_p + m_p^2}\n",
+    "$$"
    ]
   },
   {
@@ -428,7 +428,9 @@
    "source": [
     "Equivalently, from the **CM frame** perspective, since $\\vec{p}_{\\gamma} = -\\vec{p}_{p}$ and $|\\vec{p}_{\\gamma}| = |\\vec{p}_{p}|= p_{z}$, we can find out the CM total energy with expression in quantities from the CM frame is:\n",
     "\n",
-    "$\\sqrt{s} = E_0 = m_0 = |p_{z}|+\\sqrt{p_{z}^2+m_p^2}$"
+    "$$\n",
+    "\\sqrt{s} = E_0 = m_0 = |p_{z}|+\\sqrt{p_{z}^2 + m_p^2}\n",
+    "$$"
    ]
   },
   {
@@ -452,8 +454,6 @@
    "source": [
     ":::{important}\n",
     "Beam energy in the Lab frame as input value, and then we find the total energy in the CM frame and do the calculation in CM frame for analysis afterwards. \n",
-    "\n",
-    "Assuming incoming $\\gamma$ beam to stationary proton target in photo-production experiment, e.g. [GlueX](http://www.gluex.org/).\n",
     ":::"
    ]
   },